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A positive integer has 1001 digits all of which are 1 if this integer is divided by 1001 then find remainder

A positive integer has 1001 digits all of which are 1 if this integer is divided by 1001 then find remainder

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1 Answers

Srutarshi Tripathi
38 Points
9 months ago
The number N: (101002 – 1)/9 
Now, by Fermat’s Little Theorem , 101001 = 10 (mod 1001)
or, 101002 – 1 = 99 (mod 1001)
or, (101002 – 1)/9  = 11 (mod 1001)
 
Hence, THE REQUIRED REMAINDER IS 11 (ANSWER)

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